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General Tso's Chicken (deep-fried chicken in a sweet sauce) was popularized at Peng's restaurant in Manhattan on 291 East 44th Street, from about 1973-74.

The similar "General Ching's Chicken" had been served at Hunam (845 Second Avenue, near 45th Street) in 1972 and Shun Lee Palace (155 East 55th Street, near Third Avenue) in 1973.

Wikipedia: Zuo ZongtangZuo Zongtang (左宗棠; Zuǒ Zōngtáng; Tso-Tsung-t'ang; [tswɔ̀ tsʊ́ŋtʰɑ̌ŋ]; 10 November 1812 – 5 September 1885), also sometimes referred to as General Tso, was a Chinese statesman and military leader of the late Qing dynasty.

Wikipedia: General Tso's chickenGeneral Tso's chicken (pronounced [tsu̯ò]) is a sweet, slightly spicy, deep-fried chicken dish that is served in North American Chinese restaurants. The dish is named after Zuo Zongtang (formerly romanized Tso Tsung-t'ang), a Qing dynasty statesman and military leader, although there is no recorded connection to him nor is the dish known in Hunan, Zuo's home province.
(...)Peng claim
Peng's Restaurant on East 44th Street in New York City claims that it was the first restaurant in the city to serve General Tso's chicken. Since the dish (and cuisine) was new, Peng made it the house specialty in spite of the dish's commonplace ingredients. A review of Peng's in 1977 mentions that their “General Tso's chicken was a stir-fried masterpiece, sizzling hot both in flavor and temperature”.

Wang claim
New York's Shun Lee Palaces, East (155 E. 55th St.) and West (43 W. 65th St.) also says that it was the first restaurant to serve General Tso's chicken and that it was invented by a Chinese immigrant chef named T. T. Wang in 1972. Michael Tong, owner of New York's Shun Lee Palaces, says, "We opened the first Hunanese restaurant in the whole country, and the four dishes we offered you will see on the menu of practically every Hunanese restaurant in America today. They all copied from us."

It has also been argued that the two stories can be somewhat reconciled in that the current General Tso's chicken recipe—where the meat is crispy fried—was introduced by Chef Wang, but as "General Ching's chicken", a name which still has trace appearances on menus on the Internet (the identity of its namesake "General Ching" is, however, unclear); whereas the name "General Tso's chicken" traces to Chef Peng, who cooked it in a different way.

19 May 1972, Women's Wear Daily (New York, NY), "At Table: Hunam" by Pearl Bailey, pg. 13, col. 1:
Other Hunam specialties the menu lists as "first time in New York" are General Ching's Chicken, in a tinglingly hot sauce; (...) and General Bau's duckling, prepared with mushrooms and Chinese five spices in red hot sauce.

25 August 1973, Newsday (Long Island, NY), "Subtle and spicy: the food of Hunan -- Hunam Inn, Great Neck" by Barbara Rader, pg. 2A, col. 2:
A good foil to this dish is General Ching's Chicken or Ta-Chien Chicken, both hot dishes with brown sauces.

Google Books
1 October 1973, New York magazine, "The Insatiable Critic (Shun Lee Palace review) by Gael Greene, pg. 90, col. 2:
As the guiding hand behind both Hunam and Shun Lee Palace, suave and indulgent Michael Tong knew the power of an asterisk. He lured a chef from Flower Drum, imported a Hunan hand from the mainland, pared the Palace's wearying menu and brought the cooking of Hunan to East 55th Street. (...) The hot sauce of General Ching's chicken ($4.75) tingles feverishly as the menu promises.

18 March 1977, New York (NY) Times, "A Touch of Hunan, A Taste of Italy" by Mimi Sheraton, pg. C13, col. 2:
Peng's
219 East 44th Street
(...)
General Tso's chicken was a stir-fried masterpiece, sizzling hot both in flavor and temperature, and dragon and phoenix was a combination of pearly, dewy fried lobster chunks on one side of the platter and stir-fried chicken with peanuts on the other.

16 December 1977, New York (NY) Times, "Restaurants: Hunam standby and a sense of deja vu" by Mimi Sheraton, pg. C14, cols. 2-3:
Hunam
845 Second Avenue (near 45th Street)
(...)
And General Ching's chicken lacks the brilliance that dish has at Peng's, 219 East 44th Street.

Google Books
2 April 1979, New York magazine, "New York's Chinese Restaurants," pg. 51, col. 1:
* & 1/2* PENG'S
...General Tso's chicken ($7.95*), in a crisp, sweet, garlic-studded coat with scallions and ginger, is wonderful. (...) (Col. 2 -- ed.) It's 2:40 now and for all I know it may be the number-four chef manning the wok, but General Tso's chicken is garlicked to transcendence.
Peng's, 219 East 44th Street, 682-8050.

It should be noted that there were other Chinese generals. Hunam, 845 Second Avenue, at 45th Street, in New York, April 2, 1979, page 48, col. 2, served "General Gau's duckling ($7.95*).

6 February 1981, The Star-Ledger (Newark, NJ), pg. 53, col. 5 ad:
GENERAL CHING'S CHICKENA Favorite Dish At HUNAN TASTE
This Dish Is Named After The Famous 19th Century Manchu General Ching, A Native Of Hunan Province. This Succulent Masterpiece Was Created To Celebrate General Ching's Escape When Encircled By The Enemy. It Is Symbolic In Design...Diced Fried Chicken In A Famous Hot & Special Hunan Sauce & Encircled By Sauteed Broccoli. As A Result, THis Dish Has 2 Distinctive Tastes.
(Hunan Taste, 1555 St. Georges Avenue, Colonia. -- ed.)

October 1982, Gourmet, pg. 129, col. 3:
Q. Everything at the Peng Teng restaurant in New York City is delectable, but for me the outstanding dish is General Tso's chicken. Would you be so kind as to procure the recipe?
RITA SCHWARTZ
CENTERREACH, NEW YORK
(...)
A. Chef Peng gladly revealed one of the secrets of the Orient.General Tso's Chicken Peng Teng
(Chicken with Red Peppers) (...)

Two Hundred Good Restaurants:A Guide to Eating in San Francisco & the Bay Area
By Russell S. Riera and Chris Smith
Moss Publications, CA
1981(first edition 1980)
Pg. 22 (Tai Chi, 2031 Polk Street, near Broadway):Menu Specialties...General Tsuo's Chicken (a country-style dish. Pieces of chicken encased in a golden crust, and served in a light, reddish sauce that looks like liquid jewels.)
Pg. 182 (The Royal Mandarin, 234 Northgate Shopping Center):Menu Specialties...General Cho Chicken (the menu says it's "Diced Chicken Breast with Special Sauce." And the menu is very accurate--the dish's spicy sherry and ginger-scented sauce is special.)

7 January 1983, New York (NY) Times, "Restaurants: Time of change in Chinese kitchen" by Mimi Sheraton, pg. C16, cols. 2-3:
THAT change is not always progress is proved once again by the Chinese restaurant formerly known as Peng's, on 44th Street, between Second and Third Avenues, which was given a two-star rating in 1977. Renamed Peng Teng in May 1981, this spacious and attractive modern restaurant with its many comfortable private dining rooms still turns out some very good dishes. But based on five recent visits, the kitchen's performance has become markedly uneven.

Originally named for C.K. Peng, the chef who is semiretired, the restaurant's name was revised when one of his students, L.K. Teng, took over.
(...)
Crisp-skinned meaty duck, smoked over camphor wood and tea leaves, has a mellow, meaty flavor and so does the orange-glazed beef, with its spicy, caramelized veneer. A similar glaze adds textural and flavor interest to chunks of General Tso's chicken, a much more successful dish than the steamy, stringy shredded chicken with garlic sauce or the musty-flavored deep-fried crispy duck.
(...)
General Tso's prawns, though fresh and firm, are overpowered by green pepper, but scallops, either with water chestnuts and garlic sauce or with vegetables, are irresistible.

Restaurants of San Francisco
by Patricia Unterman and Stan Sesser
Chronicle Books, San Francisco
1984
Pg. 153 (Taiwan Restaurant):
Another rich chicken dish is _General Tsuo chicken_, a dish from Hunan, described as "Mao Tse-Tung's hometown famous dish."

"The Real General Tso Was No Chicken," by Anthony Ramirez, is in the City section, New York Times, May 24, 1998, pg. 6, col. 1.

December 1996, Flavor & Fortunevolume 3, no. 4, pg. 5, col. 1:GENERAL TSO--THE MYSTERY MAN
BY IRVING BEILIN CHANG
(...)
General Tso Tsung Tong (1812-1885) was born in Xiang Yin, thirty-five miles north of Changsa. He was a very famous General under the Manchu Dynasty and his military activities took him to many parts of CHina. He was a very active person and loved his food, especially meat. Everywhere he went, the local magistrates, in order to cultivate his favor, would prepare special feasts in his honor, perhaps to solicit favors and at least so that he would think kindly of them. He was a hard person to please, but try they did.(...)

Once he was sent to Xinjang on a military expedition. The people of this western border-province were mainly Muslims whose religion did not allow them to eat pork; so the general's diet was severely curtailed. Three months later when he got back, specifically to (Col. 2--ed.) Lanzhour, a big feast was served in celebration of his successful expedition. He told his associates that although he was not entertained with song and dance, this elaborate and bountiful meal more than made up for the very long and tough expedition where he had no pork to eat.

In 1875, the Dowager Tse Xi promoted him to the royal court. She held a banquest in his honor in the capital, Beijing. At that banquet, they made sure that he had double servings of all the entrees. The general would always finish his portion with one sweep of his chopsticks, as if to say, he was not impressed.

After the above banquet, one of his compatriots asked him "Old friend, at one seating you can devour so much meat. It is as the old saying goes: A general's fame is as big as his appetite. I hope that stomach of yours can live up to your fame." The general smiled and retorted: "Your people love to put words in other people's mouths. What do you know? Instead of meat you can only eat the roots of vegetables. I am lucky that I enjoy meat. Maybe one day I will be stigmatized and might even be called: The Meat Eating General."

Eater -- New YorkGeneral Tso’s Creator Dies, the Guy Fieri Effect, and More Intel
The Metropolitan Opera House’s restaurant opens for brunch, plus more news and gossip from around NYC
by Greg Morabito Dec 2, 2016, 10:44am EST
— Peng Chang-kuei, the Chinese-born chef who claimed to have invented General Tso’s chicken, died on Wednesday. He was 98. A native of the Hunan province, Peng said that he created the dish in the early 50s while working as a banquet cook for the Nationalist government in Taiwan. The chef later brought his specialty to New York in 1973 with the opening of his restaurant, Peng’s, on 44th Street. In her 1977 review, Mimi Sheraton gave the dish its first-ever mention in the Times: "General Tso's thicken was a stir‐fried masterpiece, sizzling hot both in flavor and temperature." After failing to expand his restaurant group in New York, Peng returned to China in the 80s, where he opened a Hunan-style chain that flourished.